On the construction of non- 2 -colorable uniform hypergraphs

The problem of 2 -coloring uniform hypergraphs has been extensively studied over the last few decades. An n -uniform hypergraph is not 2 -colorable if its vertices cannot be colored with two colors, Red and Blue, such that every hyperedge contains Red as well as Blue vertices. The least possible number of hyperedges in an n -uniform hypergraph which is not 2 -colorable is denoted by m ( n ) . In this paper, we consider the problem of finding an upper bound on m ( n ) for small values of n . We provide constructions which improve the existing results for some such values of n . We obtain the first improvement in the case of n = 8 .